The girl's 13-year-old brother found his sister lying in a pool of blood in the family's kitchen early on Tuesday morning, with severe injuries. Police said she had been stabbed several times.
The boy told police that his mother was standing next to the body of his sister, with a knife in her hand.
The 13-year-old ran to his neighbour's house, who called police to the apartment in Goldscheidgasse.
An ambulance and first aid helicopter arrived on the scene at 7.30am and medics tried to revive the child. “Help came too late,” a spokesman for the ambulance service, Ronald Packert said.
Police said that the child's mother appeared to be in shock and did not resist arrest. The 13-year-old boy has been taken into emergency care, according to police spokesman Patrick Maierhofer.
It is believed the children's father was not at home.
A report in the Kronen Zeitung newspaper said that the family were due to be evicted from their flat on Tuesday.
A 40-year-old neighbour told the newspaper that the family had been having financial problems and that the woman had sometimes been heard shouting at her children but had never been violent towards them. She added that she had met the woman for a coffee on Monday and had lent her €200 when she heard that they were in trouble.
The children were not registered with Vienna's Youth Welfare Office.
According to the Kronen Zeitung newspaper the girl died from stab wounds to her throat. The medical team who treated her are reported to be traumatised.
In July a woman in Vienna's Favoriten district smothered her five-year-old son with a cushion. She told police that she was depressed and had been hearing voices that told her to kill her child.